diff --git a/src/textual/driver.py b/src/textual/driver.py
index 9a7fecb271..fe26f11db1 100644
--- a/src/textual/driver.py
+++ b/src/textual/driver.py
@@ -1,7 +1,7 @@
 from __future__ import annotations
 
 import asyncio
-import shutil
+import threading
 from abc import ABC, abstractmethod
 from contextlib import contextmanager
 from pathlib import Path
@@ -229,10 +229,25 @@ def deliver_binary(
                 set the `Content-Type` header in the HTTP response.
         """
         if isinstance(binary, BinaryIO):
-            with open(save_path, "wb") as destination_file:
-                shutil.copyfileobj(binary, destination_file)
-        else:  # isinstance(binary, TextIO):
-            with open(save_path, "w", encoding=encoding) as destination_file:
-                shutil.copyfileobj(binary, destination_file)
-
-        binary.close()
+            mode = "wb"
+        else:
+            mode = "w"
+
+        def save_file_thread():
+            with open(save_path, mode) as destination_file:
+                read = binary.read
+                write = destination_file.write
+                while True:
+                    data = read(1024)
+                    if not data:
+                        break
+                    write(data)
+            binary.close()
+            self._app.call_from_thread(self._delivery_complete, save_path=save_path)
+
+        thread = threading.Thread(target=save_file_thread)
+        thread.start()
+
+    def _delivery_complete(self, save_path: Path) -> None:
+        """Called when a file has been delivered."""
+        self._app.post_message(events.DeliveryComplete(save_path=save_path))
diff --git a/src/textual/events.py b/src/textual/events.py
index 13188d6845..fb7ad263d6 100644
--- a/src/textual/events.py
+++ b/src/textual/events.py
@@ -14,6 +14,7 @@
 from __future__ import annotations
 
 from dataclasses import dataclass
+from pathlib import Path
 from typing import TYPE_CHECKING, Type, TypeVar
 
 import rich.repr
@@ -732,3 +733,11 @@ def __init__(self, text: str, stderr: bool = False) -> None:
     def __rich_repr__(self) -> rich.repr.Result:
         yield self.text
         yield self.stderr
+
+
+@dataclass
+class DeliveryComplete(Event, bubble=False):
+    """Sent to App when a file has been delivered."""
+
+    save_path: Path
+    """The save_path to the file that was delivered."""